A universal equation for calculating the energy gradient function in shear driven flows using the energy gradient theory

Abstract

The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done, and energy dissipation in unit volumetric fluid of incompressible flow is derived. A universal equation for calculating the energy gradient function in shear driven flows is presented. With the calculation of the energy gradient function which is a field variable and is considered as a local Reynolds number, the stability of a basic flow can be analyzed. The method can be applied to parallel flows, curved flows, and various complex flows.